As I consider myself to be an analyst first and foremost, I am interested in a wide range of analytical problems. However, within analysis I am most interested in Harmonic Analysis, Partial Differential Equations and Geometric Measure Theory and the connection between these areas.
More specifically, I am working on solving boundary value problems for linear elliptic and parabolic PDEs using Harmonic Analysis techniques and results from Geometric Measure Theory.
1) Ulmer, M. (2026). Solvability of the Dirichlet problem for a new class of elliptic operators. Journal of Differential Equations, 485, Article 114740. https://doi.org/10.1016/j.jde.2026.114740
2) Dindoš, M., Pipher, J., & Ulmer, M. (2025). The $L^p$ regularity problem for parabolic operators with transversally independent coefficients. Analysis & PDE (Accepted). arXiv:2509.06627
3) Dindoš, M., Sätterqvist, E., & Ulmer, M. (2024). Perturbation theory for second order elliptic operators with BMO antisymmetric part. Vietnam Journal of Mathematics, 52, 519–566. https://doi.org/10.1007/s10013-023-00653-z
Dong, H., & Ulmer, M. (2026). Nontangential maximal function estimates for the elliptic mixed boundary value problem with variable coefficients. Preprint. arXiv:2605.15414
Schikorra, A., & Ulmer, M. (2026). Failure of Calderón–Zygmund estimates for degenerate elliptic PDEs with $A_p$-weights when $p > 2$. Preprint. arXiv:2605.15414
Ulmer, M. (2025). Equivalence between solvability of the Dirichlet and Regularity problem under an $L^1\text{--}L^\infty$ condition on $\partial_t A$. Preprint. arXiv:2509.10328
Ulmer, M. (2025). Perturbation theory for the parabolic Regularity and Neumann problem. Preprint. arXiv:2408.12529
Ulmer, M. (2024). $L^p$ boundary value problems for elliptic and parabolic operators [Ph.D. thesis, University of Edinburgh]. ERA Repository. http://dx.doi.org/10.7488/era/4636